UNIT DIMENSION, VECTOR , KINEMATICS in ONE SHOT For WBJEE 2026 | Full Mechanics in One Shot | part 1

Añadido: 2026-05-11

[00:00:03]I will take What are you chocolate?

[00:01:07]Perfect. I guess you guys perfect sound boys. Perfect. Perfect.

[00:01:40]Okay. Okay. Nice. Nice.

[00:02:02]Can I start?

[00:02:05]>> Okay. So this is the first slide.

[00:02:08]Introduction is slide that I for them.

[00:02:21]This is my name and I got with some renowned coaching institute. I not taking the name and I had four years plus experience on this teaching line.

[00:02:38]Okay. So the chapters that we covered first is basic mathematics. Why I'm taking this?

[00:02:47]basic maths, vectors, unit dimension, dynamics 1D, dynamics 2D, uh, teaching experience.

[00:03:44]So that Baselory.

[00:04:16]So first thing about coordinate system what are the coordinate system and second is coordinate system and has two parts system and another is the polar coordinate systems. Okay.

[00:04:46]Systemicalordinate system.

[00:04:54]This is a one shot. So moving on to the next page. What is cartian coordinate system?

[00:05:14]What is the meaning of the word?

[00:05:26]The board is very light.

[00:05:30]Fore.

[00:05:56]So cartician coordinate systems. Cartian coordinate system.

[00:06:08]So y this one is a point this is my yaxis and this is my z ais Okay.

[00:06:57]First thing that you do that surface element d1= dy d What dy means this?

[00:07:19]This one is dz dy dz cross the cross multiplication dy dz dy dzction d s1 is nothing but the cross product of dy cross dx and d s is dx d3 dx dy dx dy okay system infinity represent a plane to y plane y Y constant Y constant plane to O XZ O XY Z constant represent O XY So next is polar coordinate systems.

[00:09:20]This is a sphere.

[00:09:28]Okay.

[00:09:34]Then how should I represent this? So there is three thing in tatisha system we studied about x y and z but here we study about r theta and zed what is zed zed is this distance r is this distance R is this distance and theta is this angle. Okay. So these are the parameters to determine the cylindrical coordinate system clear.

[00:10:20]After that we will study about the spherical systems. What actually the spherical coordinate system is that a point which we represent in the spherical sperical coordinate system is in the basis of r theta.

[00:10:35]So you can order same as which I can that is rta or rta. So this is data actually let me know what is r or somehow row this point and this is the angle phi is the angle which is measuring from z ais theta is the angle measuring from the x-axis Next transformation of systems vector system then how can I take IAP and Kap if I have if I to take unit vector in spherical polar coordinate system. Then how can I do? There must be that there are three three different things vectors three vectors 1 2 3. So one is the E P vector or P gap E theta gap and P prime. Yeah. Can you see this? These are the unit vectors of spherical coordinate systems. Okay.

[00:12:26]That is only so row sin cos theta Y = sin 5 cosin theta = cos = x + y + y and y= x² + y / as a to solve questions easily.

[00:13:41]Next to cylindrical and cylindricical to spherical. R is represented as row sin of z is represented as row cos of theta is theta. Okay. Theta is theta. Next row is = r² + square = tan inverse of r.

[00:14:17]Next question. Next part. What is this?

[00:14:21]This is not stud things because this is just a graph which I mentioned here and the equation of the graphs is like this.

[00:14:32]Okay.

[00:14:37]So these are the graphs different section. Section is nothing but a part of a part of sound.

[00:15:17]Hello session is nothing but part of sessions.

[00:15:59]time. So, Therefore, this is parabola.

[00:16:53]Angle hyperola and circle pattern.

[00:17:19]Sound is very Hello.

[00:17:56]Is it better?

[00:18:02]Is it better?

[00:18:08]Why is it better or not?

[00:18:32]The center is not at origin. It is x² - h² + y² - k² = r² where h and k is the what center of the circle. Then in a general equation x² + b y square + cx + b y + =0 where the coefficient of a x² and y square should not be zero. This is the what general equation form of next is going to be parabola y = a x - k and the vertex of this = yirect Next moving to ellipse. What is the equation of ellipse? x - h² sorry a² + y - k square by square = 1.

[00:19:42]This is ellipse where a is greater than center of focus. Focus focus.

[00:20:01]bas and Vertx 1us.

[00:21:26]What is this thing?

[00:21:29]ID of one sheet, hyper of two sheet, elliptical, elliptical parabola and parabola.

[00:21:48]for watching.

[00:22:09]Just Physics is all about x² + y².

[00:22:38]Next, next is important particular motion concept of curvature key.

[00:23:13]Okay. So radius of this r = 1 + y² by 2 / y dot dot refers to first order derivative. Y dot means dy by dx. Y dot means dy by means square. This is single dot and double dot.

[00:23:47]Okay.

[00:23:49]Okay. Okay. Okay. Okay.

[00:23:54]So this is radius of this point.

[00:24:14]You have to find the y² = 4 ax So point of center 80% If the radius of the above the RC must be less than Z radius of 29.

[00:25:47]Next.

[00:25:48]>> 34 days.

[00:26:08]That is more than sufficient.

[00:26:30]That's a visible Disex time. Slope is equals to velocity.

[00:27:22]Velocity graph. Acceleration time graph.

[00:27:26]Force mass.

[00:27:48]This is the most stable point.

[00:27:56]This is okay.

[00:28:02]So next I talking about velocity. Slope displacement graph a graph constant area is equals to change in velocity a graph is slow graph is slow generally meaningless 90% of the case that is meaningless but but but but But that is okay.

[00:29:46]Okay. Next.

[00:29:48]What is this maxability?

[00:30:01]Next. Next is the velocity of the = roo<unk>= omega t + inverse square graph.

[00:30:52]question.

[00:30:59]Integration. Integration.

[00:31:25]the sum of this volume elements.

[00:31:48]DX.

[00:31:53]VX.

[00:31:56]So that's lambda xation.

[00:32:21]I mean, That's a integration.

[00:33:13]Sorry.

[00:33:22]Perfect.

[00:34:08]This is the formula of cards.

[00:34:18]Very good. Very very good.

[00:34:48]But rather than moving on to the next part. What is this?

[00:35:10]Okay.

[00:35:14]Easy question.

[00:35:52]This is the value. This is the value.

[00:35:55]This is R. This is R. This is what this is r sin of theta by 2 and this is also r sin of 2. So very good.

[00:36:16]Okay. So this is the blind side.

[00:36:24]Next chapter.

[00:36:59]vectors. Vector vector but vector is the finest chapter.

[00:37:14]What is vector?

[00:37:18]So this is so this is the head of the vector.

[00:37:31]This is the tail of the vector.

[00:37:34]This is the magnet of and this indicates the detection of vector properties of vector that's very That's all properties of vector of vector.

[00:38:31]That is enough.

[00:38:42]opposite component of vector vector side theta side R cos theta and this one is R sin theta cos next= inverse of P sin theta / P + cos theta formula These are some vectors random for A vector plus B vector plus C vector plus D vector A and I think next identity.

[00:40:58]But of three of this four side that Sigma of cos of k= 1 - sigma of = 0 sin of 2 k = 0 I Okay. Next triangle in vector form that is RG.

[00:42:22]RG is nothing but vector B2. R A + R + R C / 3.

[00:42:33]This one is vector. This one is R vector. This one is RC vector.

[00:43:01]Take it. Then R G is equals to R1 + R + R + R4.

[00:43:24]Clear.

[00:43:26]Very good. So next product form of reflected directly question proof that this one is the reflected. Sorry, this is incident.

[00:44:15]This is incident. This is equals to Icap - 2 into Iap.

[00:44:44]What is this? This one clear everyone.

[00:45:03]40.

[00:45:07]So next find this solution.

[00:45:48]This this plus this equals to 7. Find the value of a square + U vector. U vector can be written as 2 I + 3 J + I vector V A I + B + C U V U V 2 A plus 3 B + 3 sorry 5 C 5 C Ug77.

[00:47:15]Okay. So, okay.

[00:47:29]I wish for I J I J K I cross I cross J answer J cross I answer J cross I answer Okay.

[00:48:42]42 like I measure that this is product application of cross This is a topic from vector field.

[00:49:58]If there is a flow of anything, if there is a flow, so those who are in Hindi or English medium then they also learn. So vector field what is vector field? Vector field is nothing but if there is a flow like if a river is flowing with a certain velocity if river is flowing certain velocity if air is flowing with a certain velocity if car is moving with certain velocity then they might be not having they don't have a still or a particular point they have a vector vector vector vector vector vector vector vector vector vector Yes. Write a picture.

[00:51:02]Same concept of vector field.

[00:51:24]X Y 4 X Y - 4 Y matrix Vector matrix wise vector matrix sorry satisfy reason.

[00:52:42]What is this?

[00:52:44]Nothing.

[00:52:47]So Lots of vectors, lots of equations, lots of points have created this vector field. Clear? This is the concept of vector fleet. I think you all understand this now.

[00:53:23]Is it clear?

[00:53:34]So this is the application of this concept the vector field.

[00:53:40]This is the divergence of a vector.

[00:53:43]Divergence of a vector. Okay.

[00:53:50]Divergence of a vector.

[00:54:02]Divergence of greater than this operator. This is a particular operator named as diver.

[00:54:29]This is not very divergence is this. This is the operator called divergence. Divergence is nothing but the partial differentiation partial del x iap y jc plus del z. This is actually the part the divergent of vector diverg of a vector.

[00:55:07]This is the Then divergence of V divergence of F is can be written as divergence.

[00:55:32]of fx y as f = to f_sub_x i fy g of x Y sorry XY Z function divergence is important for you. Okay.

[00:56:19]So of f is written as del x of fx del x of fy g of this del of x vance.

[00:56:53]This notap X del Y Z of FX FY X here to the = Hey, thank you.

[00:57:50]Next.

[00:57:59]There is three forces.

[00:58:08]Equilibrium of that is equilibrium of three.

[00:58:34]Ifces are acting on a body in equilibrium, then each forces is proportional to the sign angle.

[00:58:46]Then each force is proportional to the sign angle of between other two forces and their constant proportionality is same.

[00:58:57]Clear properties of triangle B.

[00:59:12]So b by sin alpha diagram = sin beta = ruby is this is r this is q and the angle is ala and beta and this is also same angle.

[01:00:05]question.

[01:00:18]Okay. So first one A= to mod Aantity quantity Next half of this is nothing but a triangle.

[01:01:02]Triangle half into a cross burst.

[01:01:15]Goodbye.

[01:01:33]Next class 10 option.

[01:02:10]Sure.

[01:02:30]H cross c. So, a dot bul a b c a dot join.

[01:02:59]So, volume executable.

[01:03:11]Next triple product that volume of this is 1x 6 of box of a A cross bals.

[01:03:38]to B C minus.

[01:04:06]So it can be as B into A C minus C into A.

[01:04:36]Is it clear?

[01:04:55]Please answer me.

[01:05:00]Please answer.

[01:05:14]Sorry.

[01:05:47]So next question Okay, let's start the question. First question of times.

[01:06:47]Ready?

[01:07:04]already.

[01:07:24]One shot cinema.

[01:07:33]Majority bits. Majority 9 8 7.

[01:08:02]C dot cross C dot A.

[01:08:19]Okay. Zero is cross and after that I will set the in 3 2 1 questions. CS question.

[01:09:53]Option C in a triangle ABC and C represent this vector.

[01:10:14]What is your name? My name is A. P is equals to A B cos theta cos theta= A / A B 3 + 2 + 1 + 2 + 1 + 5 6 / 9 + 1 + 11 ABC 3 + 3 + 9 9 2 11 1 + 4 + 6 6 question.

[01:12:40]Next question. I will start Next.

[01:13:15]And after that we start class.

[01:13:29]Okay.

[01:13:43]Option BT B is correct Yes.

[01:14:34]A B three vectors. A B C a vector X A question.

[01:15:30]time. So later chaxis.

[01:16:10]option. Option. Option.

[01:16:17]Option A.

[01:16:39]is not option. This is option.

[01:16:57]Options fast.

[01:17:21]options.

[01:17:39]What does it say?

[01:18:07]Ca* A plus beta * of B is perpendicular to C first input. X plus beta* of B C X And vector x of the form this is x dot c vector factor.

[01:19:10]This is a hint for solution of the question.

[01:19:16]Okay, next question.

[01:19:20]Hey, thank you.

[01:19:49]question.

[01:19:53]Yeah.

[01:20:05]What is that?

[01:20:10]>> You got some I understand.

[01:20:50]like this three = 3.

[01:21:02]I am here.

[01:21:15]America.

[01:21:43]object cos inverse of 5 by 9 and mod a + b = <unk>2 * a - = * g A square + mod B² - 2 into A² + B² + 2 into A B A B cos theta cos theta into 5 by 9 mod A B 5 by 9th.

[01:23:10]Next question.

[01:23:17]Next question.

[01:23:29]Start.

[01:23:32]Next question.

[01:23:44]King by 55. Yes.

[01:24:00]Hey, back back.

[01:24:19]industry and I get networked on that.

[01:25:03]What's up?

[01:25:20]That was good.

[01:26:02]vectors, OQ and O each of magnitude A. A A and A. So the resultant of three vector is this component.

[01:26:29]Easy question.

[01:26:41]That is the thing.

[01:26:54]What is this question?

[01:27:04]30 minutes.

[01:27:08]Hey type of camera.

[01:27:32]Yes.

[01:27:53]constant.

[01:28:07]Thank any chance.

[01:28:37]You have 2 minutes.

[01:29:05]This is the last second question.

[01:29:11]Next.

[01:29:28]Hey, one of the finest question.

[01:30:02]A XY Z.

[01:30:14]Tell me how.

[01:30:29]So as a free content time of stress Time this one. So xus actually First condition is the best.

[01:31:43]No one else.

[01:31:47]Sorry.

[01:31:58]Ifus falsap.

[01:32:38]So this is nothing else this one. So fus vector.

[01:32:50]So this is equals to gals vector vector g. What is G?

[01:33:13]Yes or no?

[01:33:40]XY.

[01:33:56]So this one is move on to the next.

[01:34:07]Okay.

[01:34:23]Sh 197.

[01:35:10]So that can be inserted at breaking start.

[01:36:06]Hello. Hello.

[01:36:29]Hey, hello break.

[01:36:43]Foreign speech. Foreign speech. Foreign speech.

[01:37:18]So dimension dimension mechanics.

[01:37:39]This is a short note.

[01:37:56]likes.

[01:38:13]quantities.

[01:38:44]What is the average value of total unit dimension of kinetic vector s please give me sound like that.

[01:39:19]Let's move on.

[01:39:36]That's it.

[01:39:46]Fore! Foreign! Foreign!

[01:40:10]Perfect.

[01:40:20]Hey Sound is perfect. Everything is perfect.

[01:40:39]Thank you.

[01:40:59]So about this particular thing about dimension first thing is what is the quantities *antity= xengave Because of XY XY Z XY Z there are two different quantities. One is the fundamental quantity quantity. The fundamental quantity is seven.

[01:41:32]Fundamental quantities there are seven fundamental quantities are there. What is the length? What is the mass? The time current I substance normal density.

[01:41:52]Okay. And dimensions of So there are the base and fundamental physical quantities in physics. Okay.

[01:42:17]Next.

[01:42:18]Next.

[01:42:38]Next dimension is quantity. The quantities like index refractive index sin theta cos theta x etc. Dimension quantity dimensionless.

[01:43:06]Next of dimensions. What is the principle of?

[01:43:21]Let's keep thinking principle of homogenity of dimensions.

[01:43:49]What is the principle?

[01:43:53]We want to add two quantities.

[01:43:56]Two quantities in any physical meaningful equation. The dimensions of a jets must be identical with the dimension of ls. And one thing has to be noted if there are two different dimensions then if we have to add this two dimensions then they are dimensions must be same. Okay is it clear is equals to UT. So the dimension of S is must equal to the dimension of T.

[01:44:32]And next thing if I have to write one thing that is uh uh v = u + a u = s = s = = = a² then = of dimension.

[01:45:11]Okay.

[01:45:13]Next. Next thing is the method of dimension analysis to check the correctness of an equation. Use the principle of dimensional homogenity to determine the relationship between the physical quantities.

[01:45:38]Next.

[01:45:43]So, 11.

[01:46:22]Deration of using dimensional sum. Suppose a is equivalent to Q. The power sorry Q power X r the power Y.

[01:47:04]important.

[01:47:20]quantity depends on dimension dimensional variables and these variables involves a k fundamental dimension k fundamental dimensions to the then the relation the relation can be expressed in the terms of mus k dimensionless product dimensional product dimensionless If a physical quantity depressed in terms of n minus k dimensionless products constant constant oftus.

[01:48:20]Some useful relations like this. This this this this clearing next watching 100 plus So types of errors.

[01:49:20]Next of errors subtraction add= * delta x function will be more for function of many many variable delta z + y= z into least combination of errors by important results mean absolute questions.

[01:50:15]Questions questions question. Ready everyone?

[01:50:19]Everyone ready?

[01:50:24]Hello. Everyone ready?

[01:50:49]question.

[01:50:54]First question.

[01:51:08]question.

[01:51:22]Questions question.

[01:51:37]Now question.

[01:51:59]Uh documents.

[01:52:42]Hello. Hello. Hello. Hello. Hello.

[01:52:43]Hello.

[01:53:09]Hello. Hello. Hello.

[01:53:24]Clear. So that's quite beautiful.

[01:53:46]more time.

[01:53:58]She Hey, sorry.

[01:54:35]Question volume.

[01:54:43]Speed up. Speed up. We have to speed up.

[01:54:59]Let's move ahead.

[01:55:05]side please.

[01:55:30]See Please proability probability options in status.

[01:56:02]2 into 36 question.

[01:56:20]So question police.

[01:56:49]Let me get it.

[01:57:10]Christ 25 Cutting 40 plus chocolate.

[01:58:12]Option time.

[01:58:26]Next.

[01:58:30]Let's see.

[01:58:40]What is very good?

[01:58:53]Very good.

[01:58:57]Consider this.

[01:59:26]65 at least 100.

[01:59:48]Almost without any without - homog.

[02:00:57]This type of question.

[02:01:09]The dimension of function and the angular momentum are same. Dimension of function mus same but same model.

[02:01:34]Next question.

[02:01:37]That volume 3x2 pressure Hey guys.

[02:02:27]Hey, too. Perfect.

[02:02:38]The next question is advance question.

[02:02:59]Let me ask you dimension.

[02:03:11]Visible motion visible. Are you invisible?

[02:03:36]Okay.

[02:03:58]A dimension is quantity of electronic charge E perivity of free space known L constant H speed of light C and is with the dimension This quantity is written as this and m is a nonzero integer then this r= the set of the set of alpha beta gamma delta confirm dimension mus 4 a² beta i next * gamma power equation solve for We solve the equations and after solving the equations we got alpha= to minus 2 beta is = gamma and gamma is equals to alpha from this scenario 2 minus nus very good okay so moving on to the next question this also advanc Sorry. Sorry.

[02:06:06]Okay.

[02:06:41]70.

[02:06:49]Hello. Hello.

[02:06:53]And I was about Alpha - 7 - easy questions.

[02:07:44]Okay.

[02:07:54]Give me an option.

[02:08:09]Next question.

[02:08:26]So s= to s is a physical quantum which is defined as a cross by mu where is the electric field and b is the magnetic field. mu not is the permitivity of free space and the dimension of s are the same of the dimension of the following quantities.

[02:08:54]Advanc time.

[02:09:37]option.

[02:09:41]The speaker is full of The sound.

[02:09:58]Next solution can see.

[02:10:21]Okay, move to the next question.

[02:10:27]Easy question.

[02:10:44]question.

[02:10:50]She said question number one.

[02:11:03]for watching.

[02:11:29]Hey, you are welcome to mate.

[02:11:40]How many option?

[02:12:03]Option A. Option D.

[02:12:07]Option A. Option D.

[02:12:22]Option A.

[02:12:25]Option A.

[02:12:53]= 1 B = -1 and C = 4 A1 B -1 C4 A1 - 1 C4 A1 B -1 C4 option A correct Very good.

[02:13:26]Okay. Sorry. Moving on to the next question.

[02:13:34]Last question.

[02:13:48]Next possibility.

[02:14:11]Hello. Hello. Hello.

[02:14:36]Hello. Hello. Hello. Hello. Hello.

[02:14:48]Everyone please respond.

[02:14:52]Everyone please respond.

[02:14:54]Is sound is clear.

[02:15:15]What is the frame of reference?

[02:15:39]reference. That is equals to minus into a frame with respect to the initial frame.

[02:16:00]Okay.

[02:16:02]Next= ris sorry I'm going to Delta R2 is nothing but R is nothing but instantaneous velocity V dot sorry G S dot R dot Acceleration is actually written as a next equation of motion physics. Vector is the only conant.

[02:17:49]Okay.

[02:17:52]R= U + delta RA is nothing but changement.

[02:17:58]So square= a sus and sen concept. What is this? What is the concept map called the drop velocity always check the direction of signs.

[02:18:23]Okay. Next motion v= a always v dv by d s and d by acceleration to v crossing time for some distance t is nothing but x /2 of position X1 of next import questions.

[02:19:22]Last question to solve. So see do the first question.

[02:20:00]Hey, one PDF page. PDF. finish.

[02:20:24]Option B.

[02:20:37]Hello. Short speed.

[02:21:02]Option answer 67.

[02:21:36]I I question here. Option B, option B. Very good.

[02:22:13]Option B. Option B option.

[02:22:22]Option B.

[02:22:27]into this solution.

[02:22:45]Okay.

[02:22:48]Next question.

[02:22:51]A question. One of the finest question.

[02:22:54]Okay.

[02:22:58]What is good quality of questions?

[02:23:37]already.

[02:23:43]Please tell Why you are not solving the solution?

[02:24:19]Option B.

[02:24:23]How to solve this question by dx dv by dx is a function of x y as function a= a i + Y A Z V X of del V by D X plus V Y C Y + 2 condition sorry G A I vx Vx different yus Zus partial clear.124.

[02:26:05]This is 1. This is 2 4 2 8 64 + 60 8 + 1. This is comes out 9. Option number B is correct.

[02:26:24]Next solution.

[02:26:52]like this. Is it clear? Next.

[02:26:56]Next question is a multiple choice question.

[02:27:12]mainly focus policy questions.

[02:27:16]Next question.

[02:27:31]6 67 68 this date.

[02:28:02]question last question.

[02:28:34]69 likes. One last line. Option A, B, C, D.

[02:28:38]So I'll check options.

[02:29:13]Thank you. All our kids vy = x * dx dy dt = vx X dx by dt by square * x dx by dt² X² Clear.

[02:30:24]Next question. Next is the last question.

[02:30:28]Next. Next question. Do this question.

[02:30:45]Hello.

[02:30:59]Watching action.

[02:31:29]So we will discuss in the next video.

[02:31:36]So thank you everyone for being here.

[02:31:42]Thank you for being here.

[02:31:47]option Cuss.

[02:31:52]So, thank you for being here and take care everyone. Bye-bye.

[02:32:13]Thank you everyone for being here.

[02:32:29]How was the level of the class?

[02:32:42]Thank you everyone. Take care. Bye-bye.

[02:32:44]See you in the next video, next one.

[02:32:47]Probably the next one is based on 2D motion and onwards.

[02:33:02]Thank you. Take care. Bye-bye. See you.